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\bf 36-303: Sampling, Surveys \& Society\\
HW04: Hand in on paper Thurs Apr 1, 2010
\end{center}

\noindent\ul{\em Reminders:}
\begin{itemize}
\item Please see Lecture 20, Week 10, for an outline of events for the
  rest of the semester.
\item Reading:
\begin{itemize}
\item Hill Handout on Oral Presenations
\item Bem Handout on Writing Papers
\end{itemize}
Additional information and examples are on the course website, under
the links {\tt giving talks} and {\tt writing}.

\end{itemize}

\noindent\ul{\em Exercises to Turn In (there are 4 exercises):}
\begin{enumerate}

\item {\bf Robert M. Groves Visit}.  
\begin{itemize}
\item Campus-wide lectured Noon-1pm, McConomy.  Student reception
  1-2pm.  {\em I strongly encourage you to attend.}
\item Visiting our class for Q\&A 3-430pm. {\em You must attend.}
\end{itemize}
Attend one or both of the above events, and then answer the following
questions:
\begin{enumerate}

\item Which event will you write about below? (The \ulem{noon
  lecture}, or the \ulem{class visit})

\item Write a one-paragraph summary of the talk or visit, in your own
  words.

\item Identify one interesting or noteworthy thing that you learned,
  that you didn't know before, explain why it was interesting or
  noteworthy.\\[-0.75em]

  Your description should be clear enough that I can easily remember
  it from the talk or class visit.

\item Identify one thing that you heard, that you didn't really
  understand, or you think you understood but it doesn't sound right
  to you.  If it's something you didn't understand, list one or more
  things you think you would need to know to understand it.  If it's
  something that didn't sound right to you, explain why it didn't
  sound right.\\[-0.75em]

  Your description should be clear enough that I can easily remember
  it from the talk or class visit.

\end{enumerate}




\item {\bf Cluster Sampling (Lohr, 1999, p. 170).}  An accounting firm
  is interested in estimating the error rate in a compliance audit it
  is conducting.  The population consists of 828 claims and the firm
  audits an SRS of 85 of those claims.  In each of the 85 sampled
  claims, 215 fields are checked for errors.  We can think of the
  claims as psu's (clusters) and the fields as ssu's (units), in a
  single-stage cluster sample.

Several clusters had the same number of errors, so the results of this
single-stage cluster sample can be summarized as follows:
\begin{center}
\def\z{\phantom{0}}
\begin{tabular}{ccc}
Number of claims & Number of errors & $\bar y_i$ \\
(clusters)       & out of 215 fields & $=$ (\#errors)/(\#fields) \\
\hline
\hline
\z1  & 4  & 0.01860\\
\z1  & 3  & 0.01395\\ 
\z4  & 2  & 0.09302\\ 
22 & 1  & 0.04561\\
57 & 0  & 0.00000\\
\hline
\end{tabular}
\end{center}
(data courtesy of Fritz Scheuren).  
\begin{enumerate}
\item Use the ideas about cluster sampling discussed in class and in
  the handout on cluster sampling, to estimate the {\em proportion} of
  all 828$\times$215=178,020 fields with errors in them.  Give a
  standard error for your estimate.

\item Use your answer in part (a) to estimate, and give a standard
  error for, the {\em total} number of errors in all 178,020 fields.

\item Suppose that, instead of taking a cluster sample, the firm takes
  an SRS of $(85)\cdot(215)=18,275$ fields from the $178,020$ fields
  in the population.  If the estimated error rate is the same as in
  part (a), what would the estimated variance be?  How does this
  compare to the estimated variance in part (a)?

\end{enumerate}



\item {\bf Taylor Series Variance Estimates.}  At a certain university
  there are 1998 undergraduates.  An SRS without replacement, of size
  $n=20$ is taken, to find out what is the average number of hours per
  week the students study.  Some demographic data was collected also.
  Here is the data from 20 respondents in the survey:

\begin{center}
\begin{tabular}{@{}c@{\hspace*{4em}}c@{}}
\begin{tabular}{ccc}
Sex & College & Hrs/Wk \\
\hline
\hline
M & Eng & 28 \\
M & Eng & 29 \\
M & Eng & 23 \\
M & Eng & 35 \\
M & Eng & 29 \\
M & Eng & 30 \\
M & Eng & 34 \\
M & Eng & 31 \\
F & Eng & 30 \\
F & Eng & 31 \\
\hline
\end{tabular} 
&
\begin{tabular}{ccc}
Sex & College & Hrs/Wk \\
\hline
\hline
F & Eng & 36 \\
F & Eng & 33 \\
M & Lib & 27 \\
M & Lib & 28 \\
F & Lib & 29 \\
F & Lib & 30 \\
F & Lib & 28 \\
F & Lib & 28 \\
F & Lib & 32 \\
F & Lib & 30 \\
\hline
\end{tabular}
\end{tabular}
\end{center}
\begin{enumerate}
\item Estimate the mean number of hours/wk students study at this
  university, and give the standard error.

\item Administrative records show that the total undergrad enrollment
  at the university is
\begin{center}
\begin{tabular}{c|cc}
Sex & Eng & Lib \\
\hline
M & 617 & 380 \\
F & 450 & 551 \\
\end{tabular}
\end{center}
Make four post-strata by combining sex and college of the students,
compute post-stratum weights to make the sample more representative of
the population, and compute the weighted average number of hours/wk
students study.

\item Use the Taylor Series method discussed in class to compute a
  standard error for your weighted estimate in part (b).  Compare to
  the standard error you computed in part (a).

\end{enumerate}


\item {\bf Jackknife Variance Estimates.}  Use the jackknife method
  discussed in class to compute a standard error for the weighted
  estimate in problem 3(b).  Compare to the standard errors you
  calculated in problems 3(a) and 3(c).


\end{enumerate}
\ul{\em Notes on \#3 and \#4}{\em: The sample size $n=20$ is small
  enough that you can do all the computations ``by hand'' using
  Minitab, R, Excel, etc.  If you know R and you want to compare your
  answers with the results you get from the R functions I introduced
  in class, please feel free to do so.}

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